The hypergeometric function
\(F(\mathrm {a,b;c};z)\) ,
solution of Eq. (REF ), is defined
by the series [1]}
\(F\left(\mathrm {a,b;c};z\right)=F(\mathrm {b,a;c};z)=1+\frac{\mathrm {ab}}{1!\ \mathrm {c}}z+\frac{\mathrm {a(a+1)b(b+1)}}{2!\ \mathrm {c(c+1)}}z^2+\cdots =\sum _{n=0}^{\infty }\frac{(\mathrm {a})_n(\mathrm {b})_n}{n!\;(\mathrm {c})_n}z^n,\) 
